Here, the phrase “old chants, laments about separation” is similar to an appositive. It's a phrase that gives more detail about what types of songs the speaker's father sang in the refugee camp. Though this additional information is nice, it isn't necessary to understand the sentence. You could cut out the phrase so that the sentence read, “In the camp we used to sing songs, and we prayed.” So the “old chants, laments about separation” can be understood as an aside, and set apart with dashes. Asides need to open and close with the same type of punctuation, which is why some of the other answer choices would not work.

Here, the first part of the sentence, “Because it was raining,” is a dependent clause; it cannot stand by itself as a complete sentence. The second part of the sentence, “The elementary school students had recess inside the classroom” is an independent clause; it can stand by itself as a sentence. Connecting these two types of clauses just requires a comma, not any type of fancier punctuation like a dash or a colon.

Here, we can break up the second sentence into two independent clauses, “Instead, she preferred 'Rebecca'” and “she said that name made her feel more like her own person." Both of these can be sentences in their own right. Two independent clauses can be joined by a comma followed by a conjunction, a dash, a semicolon, or, in certain cases, a colon. The only one of these pieces of punctuation offered as a possible answer is the dash, so that is the right answer.

In the underlined part of the sentence, the phrase “by then, it was already getting dark” gives extra descriptive information; however, we don't really need this extra information to understand the sentence as a whole. So, we can punctuate it as an aside, by enclosing it within dashes or parentheses. Asides have to begin and end with the same type of punctuation, so the only right answer is the one that surrounds “by then, it was already getting dark” with two dashes.

Here, the first part of the sentence, “Despite the car salesman's assurances that the used car had been inspected and showed no problems,” is a dependent clause. It cannot stand by itself as a complete sentence. The second part of the sentence, “my brother still had reservations about its safety,” is an independent clause, or a clause that can be a complete sentence by itself. To connect these two types of clauses here, we only need a comma.

Grammatically, the first sentence is fine as it is; however, the second sentence, as it is written, is a fragment. When we combine these two sentences together, we have to think about what is the most important information, and what is additional, unnecessary information. Here, you could cut out the phrase “clothes, friends, neighborhoods, ideas”, and instead write “we leave behind certain things that defined us in the past, and leaving behind these things allows us to grow and change.” We can think of the phrase we could cut out as an aside, and enclose it between two dashes. We have to introduce and close an aside using the same sort of punctuation, which is why some of the other answer choices don't work.

As it is written, the last sentence here is a fragment, so it needs to be corrected. We should connect the second and third sentences together. But how?

The phrase “Flavors that I had never imagined” continues the idea from the second sentence about how the shop had so many flavors of ice cream; however, “Flavors I had never imagined” provides extra information that isn't really necessary to understanding the sentence. We could cut that phrase out, and write, “There were so many flavors of ice cream on the menu, and it took me.” The best way to understand “Flavors I had never imagined” is to think of it as an aside, which should be enclosed in either parentheses or dashes.

This is a complex sentence, so to simplify it, we can think about which parts are most necessary and which parts are provide additional, less important information. The two flavors of ice cream that the narrator names are “worms and dirt” and “tortoiseshell.” This is important information. Following the names of the flavors are their descriptions. The descriptions are the less important, additional information, so they can be enclosed in parentheses. Using parentheses is the clearest way to rewrite this sentence, because it shows what exactly the names of the ice cream flavors are, and what the descriptions of the flavors are.

There needs to be a pause between the part of the sentence about “worms and dirt” and the part about “tortoiseshell,” which is why some of the other answers are not right.

The em-dash denotes a sudden addition to the sentence and is the only workable piece of punctuation here since what follows is not a complete sentence.

Parentheses are used to provide additional information or to include information that may serve as an aside.  In this case, the choice with the parentheses is the only choice that correctly identifies and her ever-present dog, Fido as additional information while using correct punctuation.  A comma is not necessary after Julia because Julia and her ever-present dog are only two items separated by and.  Some form of punctuation is necessary to indicate the additional information, but none of the other choices use punctuation consistently or correctly.